Theory of Machine
Balancing of rotating and reciprocating parts of an engine is necessary when it runs at

Any one of these
Moderate speed
Slow speed
Highs peed

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Theory of Machine
A rigid body, under the action of external forces, can be replaced by two masses placed at a fixed distance apart. The two masses form an equivalent dynamical system, if

All of these
The sum of the two masses is equal to the total mass of body
The center of gravity of the two masses coincides with that of the body
The sum of mass moment of inertia of the masses about their center of gravity is equal to the mass moment of inertia of the body

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Theory of Machine
For an isochronous Hartnell governor (where r₁ and r₂ = Maximum and minimum radius of rotation of balls respectively, S₁ and S₂ = Maximum and minimum force exerted on the sleeve respectively, and M = Mass on the sleeve)

(m.g - S₁)/(m.g - S₂) = r₂/r₁
(m.g + S₁)/(m.g + S₂) = r₁/r₂
S₂/S₁ = r₁/r₂
S₁/S₂ = r₁/r₂

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Theory of Machine
Which is the false statement about the properties of instantaneous center?

The double center can be denoted either by O2 or O12, but proper selection should be made
The two rigid links which have no linear velocity relative to each other at this center have the same linear velocity to the third rigid link
At the instantaneous center of rotation, one rigid link rotates instantaneously relative to another for the configuration of mechanism considered
The two rigid links have no linear velocities relative to each other at the instantaneous center

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